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Pitch space | A Wisdom Archive on Pitch space | | Pitch space A selection of articles related to Pitch space | |
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More material related to Pitch Space can be found here:
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Pitch space
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ARTICLES RELATED TO Pitch space | |
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| | |  Pitch space: Encyclopedia II - Pitch music - Need to standardize pitchThe need to standardize pitch levels, at least within one city or country, rose as performance of music which combined the organ with instrumental ensembles became more popular. One way in which pitch could be controlled was with the use of tuning forks, although even here there was variation - a tuning fork associated with Handel, dating from 1740, is pitched at A = 422.5 Hz, while a later one from 1780 is pitched at A = 409 Hz, almost a semitone lower. Nonetheless, there was a tendency towards the end of the 18th century for the frequency of ...
See also:Pitch music, Pitch music - Perception of pitch, Pitch music - Examples, Pitch music - Concert pitch, Pitch music - Varying pitch, Pitch music - Scales, Pitch music - Other musical meanings of pitch, Pitch music - Historical pitch standards, Pitch music - Need to standardize pitch, Pitch music - Changing the pitch of a vibrating string, Pitch music - Length, Pitch music - Tension, Pitch music - Density, Pitch music - Sources Read more here: » Pitch music: Encyclopedia II - Pitch music - Need to standardize pitch |
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| | | | Pitch space: Encyclopedia II - Modulatory space - Five-limit modulatory space Five limit just intonation has a modulatory space based on the fact that its pitch classes can be represented by 3a 5b, where a and b are integers. It is therefore a free abelian group with the two generators 3 and 5, and can be represented in terms of a square lattice with fifths along the horizontal axis, and major thirds along the vertical axis.
In many ways a more enlightening picture emerges if we represent it in terms of a hexagonal lattice instead; this is the Tonnetz of Hugo Riemann, discovered independen ...
See also:Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Five-limit modulatory space |
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| | | | Pitch space: Encyclopedia II - Color space - Understanding the concept Most people have heard that a wide range of colors can be created by the primary colors magenta, cyan, and yellow, if working with paints. Those colors then define a color space. We can specify the amount of red color as the X axis, the amount of blue as the Y axis, and the amount of yellow as the Z axis, giving us a three-dimensional space, wherein every possible color has a unique position.
However, this is not the only color space. For instance, when colors are displayed on a computer monitor, they are usually defined in the RGB (r ...
See also:Color space, Color space - Understanding the concept, Color space - Notes, Color space - Color space density, Color space - Partial list of color spaces, Color space - Generic color models, Color space - Commercial color spaces, Color space - Special-purpose color spaces, Color space - Obsolete color spaces Read more here: » Color space: Encyclopedia II - Color space - Understanding the concept |
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| | | | Pitch space: Encyclopedia II - Color space - Notes When formally defining a color space, the usual reference standard is the CIELAB color space, which was specifically designed to encompass all colors the average human can see. This is the most accurate color space but is too complex for everyday uses.
Since "color space" is a more specific term for a certain combination of a color model plus a color mapping function, the term "color space" tends to be used to also identify color models, since identifying a color space automatically identifies the associated color model. Inform ...
See also:Color space, Color space - Understanding the concept, Color space - Notes, Color space - Color space density, Color space - Partial list of color spaces, Color space - Generic color models, Color space - Commercial color spaces, Color space - Special-purpose color spaces, Color space - Obsolete color spaces Read more here: » Color space: Encyclopedia II - Color space - Notes |
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| | | | Pitch space: Encyclopedia II - Modulatory space - Cylindrical modulatory spaces A temperament of rank two which is not linear has one generator which is a fraction of an octave, called the period. We may represent the modulatory space of a such a temperament as n chains of generators in a circle, forming a cylinder. Here n is the number of periods in an octave.
For example, diaschismic temperament is the temperament which tempers out the diaschisma, or 2048/2025. It can be represented as two chains of slightly (3.25 to 3.55 cents) sharp fifths a half-octave apart, which can be depicted as two chains perpendicular ...
See also:Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Cylindrical modulatory spaces |
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| | | | Pitch space: Encyclopedia II - Modulatory space - Seven-limit modulatory space In similar fashion, we can define a modulatory space for seven-limit just intonation, by representing 3a 5b 7c in terms of a corresponding cubic lattice. Once again, however, a more enlightening picture emerges if we represent it instead in terms of the three-dimensional analog of the hexagonal lattice, a lattice called A3, which is equivalent to the face centered cubic lattice, or D3. Abstractly, it can be defined as the integer triples (a, b, c), associated to 3a 5bSee also: Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Seven-limit modulatory space |
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| | | | Pitch space: Encyclopedia II - Modulatory space - Toroidal modulatory spaces If we divide the octave into n parts, where n = rs is the product of two relatively prime integers r and s, we may represent every element of the tone space as the product of a certain number of "r" generators times a certain number of "s" generators; in other words, as the direct sum of two cyclic groups of orders r and s. We may now define a graph with n verticies on which the group acts, by adding an edge between to pitch classes whenever they differ by either an "r" generator or an "s" generator. The result is a graph of genus one, which is to say, a graph with a ...
See also:Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Toroidal modulatory spaces |
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| | | | Pitch space: Encyclopedia II - Color space - Understanding the concept Most people have heard that a wide range of colors can be created by the primary colors red, blue, and yellow, if working with paints. Those colors then define a color space. We can specify the amount of red color as the X axis, the amount of blue as the Y axis, and the amount of yellow as the Z axis, giving us a three-dimensional space, wherein every possible color has a unique position.
However, this is not the only color space. For instance, when colors are displayed on a computer monitor, they are usually defined in the RGB (red, ...
See also:Color space, Color space - Understanding the concept, Color space - Notes, Color space - Color space density, Color space - Partial list of color spaces, Color space - Generic color models, Color space - Commercial color spaces, Color space - Special-purpose color spaces, Color space - Obsolete color spaces Read more here: » Color space: Encyclopedia II - Color space - Understanding the concept |
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| | | | Pitch space: Encyclopedia II - Pitch music - Perception of pitch Pitch is a subjective quality and is something perceived by the human ear, as opposed to frequency, which is the physical measurement of vibration per second.
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See also:Pitch music, Pitch music - Perception of pitch, Pitch music - Examples, Pitch music - Concert pitch, Pitch music - Varying pitch, Pitch music - Scales, Pitch music - Other musical meanings of pitch, Pitch music - Historical pitch standards, Pitch music - Need to standardize pitch, Pitch music - Changing the pitch of a vibrating string, Pitch music - Length, Pitch music - Tension, Pitch music - Density, Pitch music - Sources Read more here: » Pitch music: Encyclopedia II - Pitch music - Perception of pitch |
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| | | | Pitch space: Encyclopedia II - Pitch music - Other musical meanings of pitch In atonal, twelve tone, or musical set theory a "pitch" is a specific frequency while a pitch class is all the octaves of a frequency. Pitches are named with integers because of octave and enharmonic equivalency (for example, C# and Db are the same pitch while C4 and C5 are functionally the same, one octave apart).
Discrete pitches, rather than continuously variable pitches, are virtually universal, with exceptions including "tumbling strains" (Sachs & Kunst, 1962) and "indeterminate-pitch chants" (Malm, 1967). Gliding pitches are used in most cultures, but are rela ...
See also:Pitch music, Pitch music - Perception of pitch, Pitch music - Examples, Pitch music - Concert pitch, Pitch music - Varying pitch, Pitch music - Scales, Pitch music - Other musical meanings of pitch, Pitch music - Historical pitch standards, Pitch music - Need to standardize pitch, Pitch music - Changing the pitch of a vibrating string, Pitch music - Length, Pitch music - Tension, Pitch music - Density, Pitch music - Sources Read more here: » Pitch music: Encyclopedia II - Pitch music - Other musical meanings of pitch |
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| | | | Pitch space: Encyclopedia II - Pitch music - Historical pitch standards As well as various systems of musical tuning being used to determine the relative frequency of notes in a scale, various pitch standards have been used historically to fix the absolute position of the scale. In 1955, the International Organization for Standardization fixed the frequency of the A above middle C at 440 Hz, but in the past, various frequencies have been used.
Until the 19th century, there was no concerted effort to standardize musical pitch and the levels across Europe varied widely. Even within one church, the pitch use ...
See also:Pitch music, Pitch music - Perception of pitch, Pitch music - Examples, Pitch music - Concert pitch, Pitch music - Varying pitch, Pitch music - Scales, Pitch music - Other musical meanings of pitch, Pitch music - Historical pitch standards, Pitch music - Need to standardize pitch, Pitch music - Changing the pitch of a vibrating string, Pitch music - Length, Pitch music - Tension, Pitch music - Density, Pitch music - Sources Read more here: » Pitch music: Encyclopedia II - Pitch music - Historical pitch standards |
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| | | | Pitch space: Encyclopedia II - Modulatory space - Circles of generators A basic and important example of a modulatory space is the circle of fifths. In equal temperament, twelve succesive fifths equate to seven octaves exactly, and hence in terms of pitch classes closes back to itself, forming a circle. Abstractly, this circle is a cyclic group of order twelve, and may be identified with the residue classes modulo twelve.
If we divide the octave into n equal parts, and choose an integer m<n such that m and n are relatively prime, we may obtain similar circles, which all have the structure of finite cyc ...
See also:Modulatory space, Modulatory space - Circles of generators, Modulatory space - Toroidal modulatory spaces, Modulatory space - Chains of generators, Modulatory space - Cylindrical modulatory spaces, Modulatory space - Five-limit modulatory space, Modulatory space - Seven-limit modulatory space Read more here: » Modulatory space: Encyclopedia II - Modulatory space - Circles of generators |
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| | | | Pitch space: Encyclopedia II - Pitch music - Changing the pitch of a vibrating string There are three ways to change the pitch of a vibrating string. String instruments are tuned by varying the strings' tension because adjusting length or mass per unit length is impractical.
Pitch music - Length.
Pitch can be adjusted by varying the length of the string. A longer string will result in a lower pitch and vice versa. The change in frequency is inversely proportional to the change in length:
A string twice as long will produce a t ...
See also:Pitch music, Pitch music - Perception of pitch, Pitch music - Examples, Pitch music - Concert pitch, Pitch music - Varying pitch, Pitch music - Scales, Pitch music - Other musical meanings of pitch, Pitch music - Historical pitch standards, Pitch music - Need to standardize pitch, Pitch music - Changing the pitch of a vibrating string, Pitch music - Length, Pitch music - Tension, Pitch music - Density, Pitch music - Sources Read more here: » Pitch music: Encyclopedia II - Pitch music - Changing the pitch of a vibrating string |
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| | | | Pitch space: Encyclopedia II - Pitch space - Fibered pitch space In analogy with mathematical usage, we might call a modulatory space the base space, and another space over each point of it, giving the register, a fiber. This gives what might be called a fibered picture of pitch space.
Less well known is the fact that a fibered picture of pitch space can also be obtained where the base space is a chordal space. For instance, suppose 2^a 3^b 5^c is a five-limit interval. If the base space is a chordal space of triads, and if each fiber consists of the integers, we may represent the five-limit interv ...
See also:Pitch space, Pitch space - History of pitch space, Pitch space - Fibered pitch space, Pitch space - External link Read more here: » Pitch space: Encyclopedia II - Pitch space - Fibered pitch space |
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